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Though the song had been introduced (in embryonic form) on the
tour to support 1975's, The Hissing of Summer
Lawns, "Coyote" was a significant musical departure: where
Hissing was ornate with pianos, layered vocals and
percussion, "Coyote" was stripped down to electric and acoustic
guitars and a fretless bass guitar played by legendary
virtuoso Jaco
Pastorius. In a sense, this was similar to Mitchell's early
albums, but the sound was extremely spacious, even repetitive, with
the verses made much longer and more like a long story. Thus,
although this is one of the faster-tempo songs on Hejira,
it still lasts for an even five minutes. (Most songs on Mitchell's
earliest albums were fewer than three minutes.) Mitchell's guitar
itself was in an unusual (low to high) C-G-D-F-C-E tuning -
presumably a type of open tuning designed to play a seventh,
ninth, or even eleventh chord.

Lyrically, "Coyote" is concerned with the difficulty of
establishing any sort of connection with people who come from
"different sets of circumstance" (as the song has it). In
particular it describes an encounter (which turns into a one night
stand) between the narrator (possibly meant to be Mitchell herself
as there is a reference in the lyrics to her coming home from the
studio) and "Coyote", a ranch worker. Coyote represents nature
contrasted with the narrator's big city (presumably LA) life where
"pills and powders" are necessary to "get them through this passion
play". The aforementioned line is also a reference to Bob Dylan's Rolling
Thunder Revue, which Mitchell was a part of in the fall of
1975.